On Drinfel'd associators

In 1986, in order to study the linear representations of the braid group $B\mathrm{\_}n$coming from the monodromy of the Knizhnik-Zamolodchikov differential equations,Drinfel’d introduced a class of formal power series $\mathrm{\Phi }$on noncommutative variables. These formal series can be considered as a class of associators. We here give an interpretation of them as well as some new tools over Noncommutative Evolution Equations. Asymptotic phenomena are also discussed.